Echoes that are received during the fourth wall work just like any other echoes and are not part of the deal. The memory/item would be something from the fourth wall itself - a memory of talking to someone during it or seeing someone do something/have something happen during these days, and the item would be something they were given by a visitor or made in remembrance of a visitor, etc.

And it'll be a lot like a black out - like the whole world collectively drank so much on New Year's that they have a blackout that lasts multiple days, with, in the case of the numbered, a lucid moment in the middle of it. People are free to not notice it initially, but considering that it isn't only them and people will talk about it, it is unlikely that they won't notice.